Finite Group Databasebeta

← #14680527

Subgroups — #14680527

Order 2816.

2566 conjugacy classes of subgroups.

The subgroup lattice has 822 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×D44C211yesmaximal, characteristic, complemented
2C2×#10622573C211yesmaximal, characteristic
3C2×#10622569C212yesmaximal, complemented
4#13066872C211yesmaximal, characteristic, complemented
5#13066861C211yesmaximal, characteristic, complemented
6#13066858C212yesmaximal, complemented
7#13066856C211yesmaximal, characteristic, complemented
8#13066855C212yesmaximal, complemented
9#13066843C211yesmaximal, characteristic, complemented
10(C2×D11)⋊#95C212yesmaximal, complemented
11C2×C11×#388C211yesmaximal, characteristic, complemented
12C23×C22⋊D11C2212yes—
13C23×D44C2211yescharacteristic
14C23×C4×D11C2212yes—
15C22×C11×C4⋊C4C2211yescharacteristic
16C22×C11×C22⋊C4C2211yescharacteristic
17C22×C11×C22⋊C4C2211yescharacteristic
18C22×C11×C22⋊C4C2211yescharacteristic
19C22×C42×C11C2211yescharacteristic
20C22×C22⋊Dic11C2212yes—
21C22×(C2×D11)⋊C4C2212yes—
22C22×(C2×D11)⋊C4C2212yes—
23C22×(C2×D11)⋊C4C2212yes—
24C22×(C2×D11)⋊C4C2212yes—
25C22×C4⋊Dic11C2211yescharacteristic
26C2×C4×D44—28no—
27C2×C4×D44—24no—
28C11×#388—24no—
29C2×C11×#95C2211yescharacteristic
30C2×C11×#95C2211yescharacteristic
31C2×C11⋊#95C2212yes—
32C2×C11⋊#95C2211yescharacteristic
33C2×C11⋊#95C2212yes—
34C2×C11⋊#95C2212yes—
35C2×C11⋊#95C2212yes—
36C2×C11⋊#95C2212yes—
37C2×C11⋊#95C2211yescharacteristic
38#10622573C418yescomplemented
39#10622569—28no—
40C25×C11C2311yescharacteristic
41C24×D11C2312yes—
42C23×C4×C11C2311yescharacteristic
43C23×C4×C11C2311yescharacteristic
44C23×C4×C11C2311yescharacteristic
45C23×C4×C11C2311yescharacteristic
46C23×C4×C11C2311yescharacteristic
47C23×C4×C11C2311yescharacteristic
48C22×C22⋊D11—24no—
49C22×C22⋊D11—24no—
50C22×C22⋊D11—42no—
51C22×C22⋊D11—42no—
52C22×C22⋊D11—42no—
53C22×C22⋊D11—42no—
54C22×C22⋊D11C2×C418yescomplemented
55C23×Dic11C2312yes—
56C23×Dic11C2312yes—
57C23×Dic11C2312yes—
58C22×D44—24no—
59C22×D44—24no—
60C22×D44—22no—
61C22×D44—22no—
62C22×D44C2×C414yes—
63C22×C4×D11—24no—
64C22×C4×D11—24no—
65C22×C4×D11—42no—
66C22×C4×D11—42no—
67C22×C4×D11—42no—
68C22×C4×D11—42no—
69C22×C4×D11D418yescomplemented
70C2×C11×C4⋊C4—22no—
71C2×C11×C4⋊C4—42no—
72C2×C11×C22⋊C4—22no—
73C2×C11×C22⋊C4—22no—
74C2×C11×C22⋊C4—24no—
75C2×C11×C22⋊C4—22no—
76C2×C11×C22⋊C4—22no—
77C2×C11×C22⋊C4—42no—
78C2×C11×C22⋊C4C2×C414yescomplemented
79C2×C42×C11—24no—
80C2×C42×C11D414yescomplemented
81C2×C22⋊Dic11—24no—
82C2×C22⋊Dic11—42no—
83C2×C22⋊Dic11—42no—
84C2×(C2×D11)⋊C4—24no—
85C2×(C2×D11)⋊C4—24no—
86C2×(C2×D11)⋊C4—24no—
87C2×(C2×D11)⋊C4—24no—
88C2×(C2×D11)⋊C4—24no—
89C2×(C2×D11)⋊C4—42no—
90C2×(C2×D11)⋊C4—42no—
91C2×(C2×D11)⋊C4—42no—
92C2×(C2×D11)⋊C4—42no—
93C2×(C2×D11)⋊C4—42no—
94C2×(C2×D11)⋊C4—42no—
95C2×(C2×D11)⋊C4C2×C418yescomplemented
96C2×C4⋊Dic11—22no—
97C2×C4⋊Dic11—24no—
98C4×D44—232no—
99C11×#95—22no—
100C11×#95—22no—
101C11⋊#95—24no—
102C11⋊#95—22no—
103C11⋊#95—24no—
104C11⋊#95—42no—
105C11⋊#95—42no—
106C11⋊#95—42no—
107C11⋊#95C2×C414yescomplemented
108#14299—111nomaximal, Sylow
109C24×C11—22no—
110C24×C11—21no—
111C24×C11—21no—
112C24×C11—22no—
113C24×C11—21no—
114C24×C11—22no—
115C24×C11—22no—
116C24×C11—21no—
117C24×C11—21no—
118C24×C11—21no—
119C24×C11C22×C412yes—
120C24×C11C2411yescharacteristic
121C23×D11—22no—
122C23×D11—22no—
123C23×D11—22no—
124C23×D11—22no—
125C23×D11—22no—
126C23×D11—22no—
127C23×D11—22no—
128C23×D11—22no—
129C23×D11—22no—
130C23×D11—22no—
131C23×D11—22no—
132C23×D11—22no—
133C23×D11C22×C414yes—
134C23×D11C2×D414yes—
135C23×D11#4114yes—
136C22×C4×C11—22no—
137C22×C4×C11—22no—
138C22×C4×C11—21no—
139C22×C4×C11—22no—
140C22×C4×C11—21no—
141C22×C4×C11—21no—
142C22×C4×C11—22no—
143C22×C4×C11—21no—
144C22×C4×C11—21no—
145C22×C4×C11—22no—
146C22×C4×C11—22no—
147C22×C4×C11—22no—
148C22×C4×C11—21no—
149C22×C4×C11—22no—
150C22×C4×C11—21no—
151C22×C4×C11—21no—
152C22×C4×C11—22no—
153C22×C4×C11—21no—
154C22×C4×C11—21no—
155C22×C4×C11—21no—
156C22×C4×C11—22no—
157C22×C4×C11—22no—
158C22×C4×C11—21no—
159C22×C4×C11C22×C412yes—
160C22×C4×C11C22×C412yes—
161C22×C4×C11C2×D412yes—
162C22×C4×C11C2×D412yes—
163C22×C4×C11C2×D414yes—
164C22×C4×C11C2×D412yes—
165C22×C4×C11#4112yes—
166C2×C22⋊D11—216no—
167C2×C22⋊D11—48no—
168C2×C22⋊D11—48no—
169C2×C22⋊D11—48no—
170C2×C22⋊D11—48no—
171C2×C22⋊D11—48no—
172C2×C22⋊D11—48no—
173C22×Dic11—22no—
174C22×Dic11—22no—
175C22×Dic11—22no—
176C22×Dic11—22no—
177C22×Dic11—22no—
178C22×Dic11—22no—
179C22×Dic11—22no—
180C22×Dic11—22no—
181C22×Dic11—22no—
182C22×Dic11—22no—
183C22×Dic11—22no—
184C22×Dic11—22no—
185C22×Dic11—22no—
186C22×Dic11—22no—
187C22×Dic11—22no—
188C22×Dic11—22no—
189C22×Dic11—22no—
190C22×Dic11—22no—
191C22×Dic11—22no—
192C22×Dic11C22×C414yes—
193C22×Dic11C2×D414yes—
194C2×D44—28no—
195C2×D44—28no—
196C2×D44—216no—
197C2×D44—216no—
198C2×D44—28no—
199C2×C4×D11—216no—
200C2×C4×D11—48no—
201C2×C4×D11—48no—
202C2×C4×D11—48no—
203C2×C4×D11—48no—
204C2×C4×D11—48no—
205C2×C4×D11—48no—
206C11×C4⋊C4—44no—
207C11×C22⋊C4—28no—
208C11×C22⋊C4—44no—
209C11×C22⋊C4—44no—
210C42×C11—28no—
211C22⋊Dic11—48no—
212(C2×D11)⋊C4—216no—
213(C2×D11)⋊C4—48no—
214(C2×D11)⋊C4—48no—
215(C2×D11)⋊C4—48no—
216C4⋊Dic11—28no—
217C22×C4×D4—111no—
218C2×#392—111no—
219C2×#388D1111yescharacteristic, complemented
220C2×#386—112no—
221#1442—111no—
222#1439—112no—
223#1439—111no—
224#1438—111no—
225#1438—112no—
226#1434—111no—
227C22⋊#95—112no—
228C23×C11—22no—
229C23×C11—24no—
230C23×C11—22no—
231C23×C11—24no—
232C23×C11—22no—
233C23×C11—41no—
234C23×C11—42no—
235C23×C11—41no—
236C23×C11—42no—
237C23×C11—42no—
238C23×C11—41no—
239C23×C11—42no—
240C23×C11—41no—
241C23×C11—41no—
242C23×C11—41no—
243C23×C11—42no—
244C23×C11—42no—
245C23×C11—42no—
246C23×C11—42no—
247C23×C11—42no—
248C23×C11—41no—
249C23×C11—42no—
250C23×C11—41no—
251C23×C11C23×C411yescharacteristic
252C23×C11C22×D412yes—
253C23×C11C22×D411yescharacteristic
254C23×C11C2×#4111yescharacteristic
255C23×C11C2×#4112yes—
256C23×C11H(5,𝔽2)12yes—
257C23×C11H(5,𝔽2)11yescharacteristic
258C23×C11H(5,𝔽2)12yes—
259C23×C11H(5,𝔽2)11yescharacteristic
260C23×C11H(5,𝔽2)11yescharacteristic
261C23×C112−1+411yescharacteristic
262C22×D11—24no—
263C22×D11—24no—
264C22×D11—24no—
265C22×D11—24no—
266C22×D11—24no—
267C22×D11—24no—
268C22×D11—24no—
269C22×D11—24no—
270C22×D11—24no—
271C22×D11—24no—
272C22×D11—24no—
273C22×D11—24no—
274C22×D11—24no—
275C22×D11—24no—
276C22×D11—24no—
277C22×D11—24no—
278C22×D11—24no—
279C22×D11—24no—
280C22×D11—42no—
281C22×D11—42no—
282C22×D11—42no—
283C22×D11—42no—
284C22×D11—42no—
285C22×D11—42no—
286C22×D11—42no—
287C22×D11—42no—
288C22×D11—42no—
289C22×D11—42no—
290C22×D11—42no—
291C22×D11—42no—
292C22×D11—42no—
293C22×D11—42no—
294C22×D11—42no—
295C22×D11—42no—
296C22×D11C4×D418yes—
297C2×C4×C11—24no—
298C2×C4×C11—22no—
299C2×C4×C11—22no—
300C2×C4×C11—24no—
301C2×C4×C11—24no—
302C2×C4×C11—24no—
303C2×C4×C11—22no—
304C2×C4×C11—22no—
305C2×C4×C11—22no—
306C2×C4×C11—24no—
307C2×C4×C11—22no—
308C2×C4×C11—22no—
309C2×C4×C11—22no—
310C2×C4×C11—41no—
311C2×C4×C11—41no—
312C2×C4×C11—42no—
313C2×C4×C11—42no—
314C2×C4×C11—42no—
315C2×C4×C11—41no—
316C2×C4×C11—41no—
317C2×C4×C11—42no—
318C2×C4×C11—41no—
319C2×C4×C11—41no—
320C2×C4×C11—41no—
321C2×C4×C11—41no—
322C2×C4×C11—42no—
323C2×C4×C11—42no—
324C2×C4×C11—42no—
325C2×C4×C11C4×D414yes—
326C2×C4×C11#12014yes—
327C22⋊D11—432no—
328C2×Dic11—24no—
329C2×Dic11—24no—
330C2×Dic11—24no—
331C2×Dic11—24no—
332C2×Dic11—24no—
333C2×Dic11—24no—
334C2×Dic11—42no—
335C2×Dic11—42no—
336C2×Dic11—42no—
337C2×Dic11—42no—
338C2×Dic11—42no—
339C2×Dic11—42no—
340C2×Dic11—42no—
341C2×Dic11—42no—
342C2×Dic11—42no—
343C2×Dic11—42no—
344C2×Dic11—42no—
345C2×Dic11—42no—
346C2×Dic11—42no—
347C2×Dic11—42no—
348C2×Dic11—42no—
349D44—232no—
350C4×D11—432no—
351C23×D4—112no—
352C23×D4—111no—
353C24×C4—112no—
354C2×C4×D4—228no—
355C2×C4×D4—224no—
356C22×C4⋊C4—111no—
357C22×C4⋊C4C2×D1111yescharacteristic
358C22×C22⋊C4—112no—
359C22×C22⋊C4—112no—
360C22×C22⋊C4—112no—
361C22×C22⋊C4—112no—
362C22×C22⋊C4—112no—
363C22×C22⋊C4C2×D1111yescharacteristic
364C22×C22⋊C4C2×D1111yescharacteristic
365C22×C22⋊C4C2×D1111yescharacteristic
366C22×C42C2×D1111yescharacteristic
367#392—118no—
368#388—24no—
369#386—228no—
370C2×#95—111no—
371C2×#95—112no—
372C2×#95—111no—
373C2×#95—112no—
374C2×#95—112no—
375C2×#95—112no—
376C2×#95—112no—
377C2×#95C2×D1111yescharacteristic
378C2×#95C2×D1111yescharacteristic
379C22×C11—44no—
380C22×C11—42no—
381C22×C11—44no—
382C22×C11—42no—
383C22×C11—42no—
384C22×C11—81no—
385C22×C11—81no—
386C22×C11—82no—
387C22×C11—81no—
388C22×C11—82no—
389C22×C11—81no—
390C22×C11C2×C4×D411yescharacteristic
391C22×C11C2×C4×D412yes—
392C22×C11#51811yescharacteristic
393C22×C11#51812yes—
394C22×C11#52011yescharacteristic
395C22×C11C2×#12011yescharacteristic
396C22×C11#52512yes—
397C22×C11#52511yescharacteristic
398C22×C11#53412yes—
399C22×C11#53412yes—
400C22×C11#53511yescharacteristic
401C22×C11#53511yescharacteristic
402C22×C11#53511yescharacteristic
403C22×C11#53512yes—
404C22×C11#53711yescharacteristic
405C22×C11#53712yes—
406C22×C11#53812yes—
407C22×C11#53812yes—
408C22×C11#53812yes—
409C22×C11#53912yes—
410C22×C11#54011yescharacteristic
411C22×C11#54012yes—
412C22×C11#54211yescharacteristic
413C2×D11—28no—
414C2×D11—28no—
415C2×D11—28no—
416C2×D11—44no—
417C2×D11—44no—
418C2×D11—44no—
419C2×D11—44no—
420C2×D11—44no—
421C2×D11—44no—
422C2×D11—44no—
423C2×D11—44no—
424C2×D11—44no—
425C2×D11—44no—
426C2×D11—44no—
427C2×D11—44no—
428C4×C11—24no—
429C4×C11—24no—
430C4×C11—42no—
431C4×C11—42no—
432C4×C11—81no—
433C4×C11—81no—
434Dic11—44no—
435Dic11—44no—
436Dic11—82no—
437C25—112no—
438C25C22×D1111yescharacteristic
439C22×D4—118no—
440C22×D4—114no—
441C22×D4—224no—
442C22×D4—224no—
443C22×D4—224no—
444C22×D4—224no—
445C22×D4—222no—
446C22×D4—222no—
447C22×D4—442no—
448C22×D4—442no—
449C22×D4—442no—
450C22×D4—442no—
451C23×C4—112no—
452C23×C4—112no—
453C23×C4—118no—
454C23×C4—112no—
455C23×C4—224no—
456C23×C4—224no—
457C23×C4—442no—
458C23×C4—442no—
459C23×C4—442no—
460C23×C4—442no—
461C23×C4C22×D1111yescharacteristic
462C23×C4C22×D1111yescharacteristic
463C23×C4C22×D1111yescharacteristic
464C23×C4C22×D1111yescharacteristic
465C23×C4C22×D1111yescharacteristic
466C23×C4C22×D1111yescharacteristic
467C4×D4—2232no—
468C2×C4⋊C4—22no—
469C2×C4⋊C4—42no—
470C2×C4⋊C4—224no—
471C2×C4⋊C4—222no—
472C2×C22⋊C4—22no—
473C2×C22⋊C4—22no—
474C2×C22⋊C4—24no—
475C2×C22⋊C4—22no—
476C2×C22⋊C4—22no—
477C2×C22⋊C4—42no—
478C2×C22⋊C4—118no—
479C2×C22⋊C4—224no—
480C2×C22⋊C4—224no—
481C2×C22⋊C4—224no—
482C2×C22⋊C4—224no—
483C2×C22⋊C4—224no—
484C2×C22⋊C4—224no—
485C2×C22⋊C4—442no—
486C2×C22⋊C4—442no—
487C2×C22⋊C4—442no—
488C2×C22⋊C4—442no—
489C2×C22⋊C4—442no—
490C2×C22⋊C4—442no—
491C2×C22⋊C4—442no—
492C2×C22⋊C4—442no—
493C2×C22⋊C4C4×D1114yescomplemented
494C2×C42—24no—
495C2×C42C22⋊D1114yescomplemented
496#95—22no—
497#95—22no—
498#95—114no—
499#95—224no—
500#95—222no—
501#95—224no—
502#95—442no—
503#95—442no—
504#95—442no—
505C2×C11—82no—
506C2×C11C4×#12011yescharacteristic
507C2×C11#232112yes—
508C2×C11#232411yescharacteristic
509C2×C11#232512yes—
510C2×C11#232811yescharacteristic
511C2×C11#261311yescharacteristic
512C2×C11#261511yescharacteristic
513C2×C11#263012yes—
514C2×C11#263111yescharacteristic
515C2×C11#263512yes—
516C2×C11#263611yescharacteristic
517D11—48no—
518C24—21no—
519C24—22no—
520C24—22no—
521C24—22no—
522C24—21no—
523C24—22no—
524C24—21no—
525C24—21no—
526C24—21no—
527C24—21no—
528C24—114no—
529C24—114no—
530C24—114no—
531C24—222no—
532C24—222no—
533C24—222no—
534C24—222no—
535C24—222no—
536C24—222no—
537C24—222no—
538C24—222no—
539C24—222no—
540C24—222no—
541C24—222no—
542C24—222no—
543C24C2×C4×D1112yes—
544C24C23×D1111yescharacteristic
545C2×D4—2216no—
546C2×D4—228no—
547C2×D4—2216no—
548C2×D4—228no—
549C2×D4—2216no—
550C2×D4—228no—
551C2×D4—448no—
552C2×D4—448no—
553C2×D4—448no—
554C2×D4—448no—
555C2×D4—448no—
556C2×D4—448no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—21no—
567C22×C4—22no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—114no—
581C22×C4—114no—
582C22×C4—222no—
583C22×C4—222no—
584C22×C4—222no—
585C22×C4—222no—
586C22×C4—222no—
587C22×C4—222no—
588C22×C4—222no—
589C22×C4—222no—
590C22×C4—222no—
591C22×C4—222no—
592C22×C4—222no—
593C22×C4—222no—
594C22×C4—2216no—
595C22×C4—222no—
596C22×C4—222no—
597C22×C4—222no—
598C22×C4—222no—
599C22×C4—222no—
600C22×C4—222no—
601C22×C4—222no—
602C22×C4—448no—
603C22×C4—448no—
604C22×C4—448no—
605C22×C4—448no—
606C22×C4—448no—
607C22×C4—448no—
608C22×C4C2×C4×D1112yes—
609C22×C4C2×C4×D1112yes—
610C22×C4#433912yes—
611C22×C4D4×D1114yes—
612C22×C4C2×C22⋊D1112yes—
613C22×C4C2×C22⋊D1112yes—
614C22×C4C2×C22⋊D1112yes—
615C4⋊C4—44no—
616C4⋊C4—228no—
617C22⋊C4—28no—
618C22⋊C4—44no—
619C22⋊C4—44no—
620C22⋊C4—2216no—
621C22⋊C4—448no—
622C22⋊C4—448no—
623C22⋊C4—448no—
624C22⋊C4—448no—
625C42—28no—
626C11#1429911yescharacteristic, complemented, Sylow
627C23—22no—
628C23—22no—
629C23—22no—
630C23—24no—
631C23—24no—
632C23—42no—
633C23—42no—
634C23—41no—
635C23—41no—
636C23—41no—
637C23—42no—
638C23—41no—
639C23—42no—
640C23—41no—
641C23—41no—
642C23—41no—
643C23—41no—
644C23—42no—
645C23—42no—
646C23—42no—
647C23—42no—
648C23—42no—
649C23—42no—
650C23—118no—
651C23—224no—
652C23—224no—
653C23—224no—
654C23—224no—
655C23—224no—
656C23—224no—
657C23—224no—
658C23—224no—
659C23—224no—
660C23—224no—
661C23—224no—
662C23—224no—
663C23—224no—
664C23—224no—
665C23—224no—
666C23—224no—
667C23—224no—
668C23—224no—
669C23—442no—
670C23—442no—
671C23—442no—
672C23—442no—
673C23—442no—
674C23—442no—
675C23—442no—
676C23—442no—
677C23—442no—
678C23—442no—
679C23—442no—
680C23—442no—
681C23—442no—
682C23—442no—
683C23—442no—
684C23—442no—
685C23C22×C4×D1111yescharacteristic
686C23C2×#433911yescharacteristic
687C23C2×D4×D1112yes—
688C23#6703712yes—
689C23#41×D1112yes—
690C23#6704211yescharacteristic
691C23#6704212yes—
692C23#6704211yescharacteristic
693C23#6704211yescharacteristic
694C23#6704311yescharacteristic
695C23C22×C22⋊D1111yescharacteristic
696D4—2232no—
697D4—4432no—
698C2×C4—22no—
699C2×C4—24no—
700C2×C4—24no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—24no—
705C2×C4—24no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—24no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—41no—
712C2×C4—42no—
713C2×C4—41no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—224no—
727C2×C4—224no—
728C2×C4—224no—
729C2×C4—224no—
730C2×C4—224no—
731C2×C4—224no—
732C2×C4—4432no—
733C2×C4—442no—
734C2×C4—442no—
735C2×C4—442no—
736C2×C4—442no—
737C2×C4—442no—
738C2×C4—442no—
739C2×C4—442no—
740C2×C4—442no—
741C2×C4—442no—
742C2×C4—442no—
743C2×C4—442no—
744C2×C4—442no—
745C2×C4—442no—
746C2×C4—442no—
747C2×C4—442no—
748C2×C4C4×C22⋊D1114yes—
749C2×C4#6699014yes—
750C22—42no—
751C22—44no—
752C22—42no—
753C22—44no—
754C22—42no—
755C22—82no—
756C22—81no—
757C22—82no—
758C22—81no—
759C22—81no—
760C22—81no—
761C22—228no—
762C22—228no—
763C22—228no—
764C22—444no—
765C22—444no—
766C22—444no—
767C22—444no—
768C22—444no—
769C22—444no—
770C22—444no—
771C22—444no—
772C22—444no—
773C22—444no—
774C22—444no—
775C22—444no—
776C22#1062305211yescharacteristic
777C22#1062305411yescharacteristic
778C22#1062306511yescharacteristic
779C22#1062306611yescharacteristic
780C22C4×D4×D1112yes—
781C22#1062307612yes—
782C22#1062307812yes—
783C22#1062309312yes—
784C22#1062313812yes—
785C22#1062313912yes—
786C22#1062318412yes—
787C22#1062318412yes—
788C22#1062320912yes—
789C22#1062320912yes—
790C22#1062323512yes—
791C22#1062323812yes—
792C22C2×C4×C22⋊D1111yescharacteristic
793C22C2×#6699011yescharacteristic
794C22#1062333611yescharacteristic
795C22#1062335911yescharacteristic
796C22#1062336111yescharacteristic
797C22#1062336111yescharacteristic
798C22#1062336411yescharacteristic
799C4—24no—
800C4—24no—
801C4—42no—
802C4—42no—
803C4—81no—
804C4—81no—
805C4—444no—
806C4—444no—
807C4—882no—
808C2—82no—
809C2—448no—
810C2C4×#6699011yescharacteristic
811C2#1307127812yes—
812C2#1307130911yescharacteristic
813C2#1307132012yes—
814C2#1307133811yescharacteristic
815C2#1307433211yescharacteristic
816C2#1307434111yescharacteristic
817C2#1307446312yes—
818C2#1307446911yescharacteristic
819C2#1307450712yes—
820C2#1307451311yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC2×C11×#388C2
socle, cosocleC24×C11C24
prime radicalC2×#10622573C2
hypercenterC2×#388D11
hypocenterC11#14299
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#388

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C22×C4×D44C2semidirect
3. C2×#10622569C2semidirect
4. #13066872C2semidirect
5. #13066861C2semidirect
6. #13066858C2semidirect
7. #13066856C2semidirect
8. #13066855C2semidirect
9. #13066843C2semidirect
10. (C2×D11)⋊#95C2semidirect
11. C2×C11×#388C2semidirect
38. #10622573C4semidirect
54. C22×C22⋊D11C2×C4semidirect
69. C22×C4×D11D4semidirect
78. C2×C11×C22⋊C4C2×C4semidirect
80. C2×C42×C11D4semidirect
95. C2×(C2×D11)⋊C4C2×C4semidirect
107. C11⋊#95C2×C4semidirect
219. C2×#388D11semidirect
493. C2×C22⋊C4C4×D11semidirect
495. C2×C42C22⋊D11semidirect
626. C11#14299semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C22×C4×D442
C2×#106225732
C2×#106225692
#130668722
#130668612
#130668582
#130668562
#130668552
#130668432
(C2×D11)⋊#952
C2×C11×#3882
#1429911